Causal Effects and Experiments

GVPT399F: Power, Politics, and Data

Causes and effects

Our goal is to better understand what factors lead to certain outcomes of interest.

  • Does increasing the number of voting booths close to a potential voter make that person more likely to vote?

  • Do peace treaties signed with factionalized rebel groups more often lead to a return to conflict than those signed with a single, cohesive group?

  • Does trade between two countries make war between them less likely?

Causes and effects

These are causal statements:

  • More local voting booths \(\rightarrow\) More likely to vote

  • More factionalization \(\rightarrow\) More likely to restart conflict

  • Trade \(\rightarrow\) Less likely to go to war

How to identify causes and their effects

Proving that changes to one factor cause changes to another is very tricky!

  • Need to account for all the other factors

The efficacy of international election monitors

Do international monitors cause less election-day fraud in democratic elections?

  • Number of elections monitored by international observers exploded throughout the 2000s

  • But do monitors increase the chances the election will be free and fair?

  • In other words, are they effective?

The efficacy of international election monitors

Dr Susan Hyde set out to answer this very question. From her article (page 39):

If the presence of international observers causes a reduction in election-day fraud, the effect of observers should be visible at the subnational level by comparing polling stations that were visited by observers with those that were not visited. More specifically, if international monitoring reduces electionday fraud directly, all else held equal, the cheating parties should gain less of their ill-gotten vote share in polling stations that were visited by international monitors.

Causal relationships

Refers to the directional connection between a change in one variable and a corresponding change in another.

  • The direction matters!

  • Treatment variable: the variable causing changes to another variable.

  • Outcome variable: the variable changing as a result of changes to another variable (the treatment).

Treatment and outcome variables

We want to test whether the presence of international monitors (treatment) leads to less election day fraud (outcome).

International election monitors present at polling stations \(\rightarrow\) Less election-day fraud at that station

Treatment variable

At any given polling station in any given election, monitors may be: 1) present, or 2) not present.

Two different conditions:

  • Treatment: condition with treatment (monitors are present)

  • Control: condition without treatment (monitors are not present)

Outcome variable

At any given polling station in any given election, fraud may: 1) occur, or 2) not occur.

Observing our outcome

Sometimes it can be hard to observe our outcome of interest.

  • How might we see all election-day fraud?

  • How might we measure it?

Observing our outcome

Hyde’s answer: vote-share!

International election monitors present at polling stations \(\rightarrow\) Less election-day fraud at that station \(\rightarrow\) Lower vote-share for the cheating party

Individual causal effects

We want to know whether the treatment causes a change in our outcome of interest.

What might this look like in the real world?

  • Imagine we are looking at a specific election

  • Five polling stations

Parallel worlds

Hypothetical election

ID Monitored vote % Non-monitored vote %
1 55.55 92.55
2 34.44 80.14
3 22.81 75.32
4 39.34 91.04
5 36.56 87.55

Individual effects

The only difference between these two conditions is the presence of international monitors!

  • The difference between vote shares under these conditions is caused by the monitors.

Individual effects

ID Monitored vote % Non-monitored vote % Difference (%)
1 55.55 92.55 -37.00
2 34.44 80.14 -45.70
3 22.81 75.32 -52.51
4 39.34 91.04 -51.70
5 36.56 87.55 -50.99

No parallel worlds

Sadly for us, we cannot create parallel worlds…

What now?

ID Monitored Monitored vote % Non-monitored vote % Difference
1 0 NA 92.55 NA
2 1 34.44 NA NA
3 1 22.81 NA NA
4 1 39.34 NA NA
5 0 NA 87.55 NA

Average causal effects

We need to move away from looking at individuals and start to look for patterns in our group.

Back to our parallel worlds

ID Monitored vote % Non-monitored vote % Difference
1 55.55 92.55 -37.00
2 34.44 80.14 -45.70
3 22.81 75.32 -52.51
4 39.34 91.04 -51.70
5 36.56 87.55 -50.99

Difference of averages across all individuals

What was the average vote share received in each world?

Avg. monitored vote % Avg. non-monitored vote % Difference
37.74 85.32 -47.58

Back to reality

ID Monitored Monitored vote % Non-monitored vote % Difference
1 0 NA 92.55 NA
2 1 34.44 NA NA
3 1 22.81 NA NA
4 1 39.34 NA NA
5 0 NA 87.55 NA

Difference-of-means

What was the average vote share received in each group?

Avg. monitored vote % Avg. non-monitored vote % Difference
32.2 90.05 -57.85

How on Earth does this work so well?

Randomization!

  • Monitors were assigned to polling stations randomly (for example, with the flip of a coin)

  • This created two groups of stations that were roughly identical on average to one another prior to treatment

  • This mimics what happens when we split our world into two (creating two literally identical groups)

Our goal

We want two groups that are completely identical to one another prior to treatment.

  • This allows us to compare their outcomes after treatment and claim that the treatment caused differences in those outcomes (if any differences exist)

Our goal

Next best thing

Instead, we should try to make two groups that are as similar as possible to each other prior to treatment.

The magic of randomization

Perfectly random assignment does this very well!

Don’t take my word for it

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Our group

ID Height Weight Eye colour
1 173.45 73.86 Brown
2 171.20 82.76 Brown
3 169.17 89.81 Blue
4 160.84 84.11 Green
5 168.63 61.80 Blue
6 173.98 61.88 Grey
7 175.75 84.49 Brown
8 168.20 91.06 Green
9 169.30 80.46 Grey
10 170.34 76.69 Brown
11 175.33 91.66 Brown
12 167.36 72.74 Grey
13 166.85 75.69 Blue
14 174.38 81.74 Blue
15 168.31 82.23 Green
16 164.81 92.85 Blue
17 171.25 60.05 Blue
18 165.36 67.49 Brown
19 160.41 88.42 Blue
20 160.96 107.84 Brown
21 167.34 89.94 Blue
22 171.54 79.48 Grey
23 173.57 89.41 Blue
24 173.71 88.52 Brown
25 172.66 79.96 Brown
26 169.52 88.86 Brown
27 163.50 68.28 Blue
28 168.48 81.98 Blue
29 164.35 87.85 Blue
30 162.19 75.48 Blue
31 178.65 109.53 Green
32 189.11 78.97 Blue
33 183.09 94.75 Brown
34 167.40 69.23 Blue
35 172.81 94.88 Grey
36 166.64 85.56 Green
37 162.36 93.31 Grey
38 177.32 103.56 Green
39 168.89 92.06 Brown
40 167.62 91.22 Grey
41 169.44 82.05 Brown
42 174.97 68.02 Blue
43 163.78 73.14 Brown
44 171.69 85.26 Blue
45 174.44 74.24 Brown
46 170.05 83.29 Green
47 174.65 95.44 Grey
48 179.14 86.37 Green
49 165.76 86.68 Brown
50 182.30 87.00 Green
51 162.06 67.21 Green
52 178.82 77.39 Brown
53 178.98 77.95 Grey
54 179.42 70.76 Brown
55 153.02 82.95 Grey
56 170.71 82.41 Green
57 162.25 101.52 Blue
58 175.05 81.48 Grey
59 171.09 99.20 Green
60 175.87 71.32 Blue
61 174.60 99.47 Blue
62 164.20 95.72 Blue
63 174.43 89.02 Blue
64 174.93 94.43 Brown
65 163.43 76.36 Grey
66 173.69 82.44 Brown
67 167.03 95.10 Brown
68 180.92 65.69 Grey
69 166.13 74.62 Grey
70 170.61 79.36 Brown
71 171.89 85.33 Grey
72 174.60 75.08 Brown
73 161.76 96.19 Blue
74 166.41 79.60 Brown
75 159.30 85.65 Grey
76 170.68 68.50 Grey
77 178.82 103.01 Brown
78 171.23 72.80 Blue
79 171.87 86.64 Brown
80 167.73 86.78 Blue
81 152.91 58.76 Grey
82 165.75 80.79 Green
83 180.13 78.20 Brown
84 166.88 68.26 Green
85 174.90 78.43 Brown
86 160.65 92.92 Grey
87 170.25 82.33 Grey
88 169.09 84.70 Brown
89 168.24 79.26 Grey
90 154.54 79.51 Grey
91 166.62 95.73 Blue
92 166.42 80.47 Blue
93 162.24 98.14 Brown
94 170.64 66.14 Brown
95 168.31 68.54 Grey
96 174.19 89.41 Brown
97 168.03 65.94 Green
98 175.91 78.36 Grey
99 165.17 78.72 Grey
100 169.90 83.44 Blue
101 161.45 55.73 Green
102 167.96 65.53 Grey
103 174.53 95.19 Green
104 168.39 59.57 Brown
105 168.84 86.82 Brown
106 172.64 69.87 Grey
107 161.84 94.73 Blue
108 174.74 73.80 Green
109 169.04 76.86 Green
110 163.32 87.11 Green
111 162.61 96.64 Brown
112 158.09 81.20 Green
113 162.54 76.78 Blue
114 163.32 89.73 Blue
115 182.62 80.61 Green
116 167.86 71.94 Grey
117 160.94 96.77 Brown
118 160.88 88.32 Grey
119 174.88 76.31 Grey
120 174.63 77.30 Blue
121 171.78 67.83 Brown
122 162.31 104.22 Blue
123 168.01 75.26 Brown
124 173.51 90.91 Brown
125 176.61 79.92 Green
126 183.67 76.64 Blue
127 172.52 60.35 Grey
128 175.89 60.79 Blue
129 179.04 92.83 Grey
130 171.05 84.72 Blue
131 175.13 90.78 Green
132 170.60 66.63 Blue
133 178.41 80.15 Green
134 169.75 101.33 Green
135 174.22 81.59 Blue
136 163.76 88.59 Green
137 163.97 74.97 Blue
138 169.01 69.57 Grey
139 163.66 66.33 Grey
140 178.45 86.64 Green
141 161.76 74.41 Grey
142 165.75 89.09 Grey
143 167.26 79.58 Green
144 171.72 65.73 Green
145 153.68 83.54 Green
146 178.65 80.13 Blue
147 170.01 74.77 Blue
148 180.43 78.88 Blue
149 172.31 90.28 Green
150 172.52 69.81 Brown
151 180.87 81.44 Grey
152 171.10 82.99 Brown
153 167.91 92.30 Grey
154 180.24 88.78 Green
155 163.82 92.91 Blue
156 183.38 101.13 Brown
157 166.42 66.69 Brown
158 168.02 78.51 Grey
159 167.82 72.85 Blue
160 171.99 85.06 Blue
161 174.39 84.77 Blue
162 170.32 75.92 Brown
163 164.61 71.85 Grey
164 175.64 68.39 Green
165 164.83 102.98 Green
166 170.33 57.28 Blue
167 161.23 77.74 Green
168 173.52 73.38 Green
169 176.69 63.00 Green
170 164.07 98.37 Blue
171 172.38 93.84 Blue
172 166.35 72.34 Brown
173 170.80 98.98 Blue
174 168.92 58.21 Grey
175 173.46 82.15 Green
176 169.92 76.43 Blue
177 166.77 87.38 Green
178 170.77 85.85 Brown
179 176.61 93.23 Grey
180 174.08 61.97 Grey
181 174.91 82.72 Brown
182 172.56 77.29 Blue
183 159.82 96.85 Brown
184 162.81 70.48 Blue
185 167.02 79.58 Brown
186 174.08 63.44 Brown
187 173.42 77.79 Green
188 172.97 86.20 Green
189 179.27 81.40 Blue
190 174.08 76.52 Brown
191 174.11 100.66 Grey
192 154.08 88.66 Blue
193 168.62 94.02 Brown
194 178.32 77.77 Brown
195 157.79 83.08 Blue
196 167.62 86.16 Green
197 164.88 86.24 Blue
198 175.96 79.34 Blue
199 167.30 100.40 Grey
200 165.43 88.86 Green
201 173.86 77.92 Brown
202 172.50 90.38 Brown
203 170.04 76.45 Grey
204 167.18 97.95 Blue
205 167.91 72.21 Grey
206 178.22 76.72 Grey
207 176.15 79.42 Grey
208 172.54 94.96 Grey
209 178.82 60.34 Brown
210 166.46 66.00 Blue
211 173.58 64.05 Grey
212 159.74 68.48 Brown
213 171.41 70.93 Grey
214 171.62 84.84 Blue
215 176.97 87.27 Brown
216 175.78 79.58 Grey
217 166.73 91.19 Green
218 157.30 84.93 Brown
219 171.34 75.14 Blue
220 174.03 77.78 Blue
221 165.89 79.50 Brown
222 169.68 61.93 Grey
223 167.15 91.26 Blue
224 168.99 83.72 Green
225 162.50 79.92 Green
226 168.25 93.30 Grey
227 158.27 76.53 Grey
228 166.77 84.01 Grey
229 168.67 77.13 Blue
230 164.65 89.50 Grey
231 177.11 86.97 Green
232 164.51 88.50 Grey
233 164.53 76.64 Grey
234 170.51 64.43 Brown
235 168.39 84.78 Green
236 175.22 84.01 Green
237 172.70 86.52 Grey
238 174.97 88.79 Green
239 164.25 88.15 Blue
240 172.24 83.19 Grey
241 170.10 83.14 Green
242 174.25 67.54 Green
243 167.71 77.09 Blue
244 161.36 82.99 Brown
245 168.73 67.83 Grey
246 170.17 81.58 Grey
247 163.32 60.32 Brown
248 161.34 64.74 Blue
249 171.71 65.06 Blue
250 173.65 71.28 Grey
251 175.38 77.53 Green
252 171.41 93.20 Blue
253 162.23 71.87 Green
254 165.28 71.08 Green
255 176.03 73.84 Blue
256 166.92 90.06 Blue
257 171.92 79.80 Brown
258 179.09 69.54 Grey
259 165.17 72.89 Grey
260 176.35 72.22 Brown
261 169.70 96.82 Blue
262 180.08 80.36 Brown
263 163.58 67.68 Blue
264 160.75 75.41 Grey
265 167.63 80.69 Brown
266 165.63 76.11 Green
267 163.03 66.29 Blue
268 169.24 82.12 Green
269 179.12 66.83 Grey
270 166.23 69.41 Blue
271 175.88 80.03 Grey
272 163.63 89.07 Blue
273 178.82 74.74 Brown
274 162.15 80.24 Grey
275 171.92 82.73 Brown
276 169.85 68.37 Grey
277 161.07 63.53 Blue
278 176.34 60.49 Blue
279 169.34 62.16 Brown
280 169.73 62.84 Green
281 178.60 68.12 Brown
282 171.29 77.29 Brown
283 163.97 84.08 Blue
284 169.28 80.53 Blue
285 184.22 85.39 Blue
286 167.97 68.20 Brown
287 173.72 87.45 Green
288 181.11 71.78 Blue
289 177.23 70.39 Brown
290 180.28 79.57 Grey
291 169.33 75.46 Green
292 165.44 80.76 Brown
293 172.72 82.62 Brown
294 169.79 95.60 Blue
295 179.75 94.71 Grey
296 171.56 68.92 Brown
297 167.61 84.67 Green
298 167.04 80.70 Green
299 174.10 70.29 Green
300 158.37 63.09 Blue
301 179.77 98.14 Brown
302 175.21 82.67 Blue
303 168.50 91.33 Brown
304 168.49 100.35 Blue
305 169.18 88.89 Brown
306 165.83 84.71 Brown
307 165.24 64.29 Green
308 176.84 62.44 Grey
309 166.06 86.83 Grey
310 173.62 79.87 Grey
311 168.91 109.09 Blue
312 168.28 95.76 Blue
313 163.57 87.42 Grey
314 171.68 71.21 Green
315 173.75 90.77 Blue
316 158.63 82.57 Grey
317 167.24 82.08 Green
318 165.27 78.51 Blue
319 184.60 54.18 Blue
320 160.77 72.17 Grey
321 183.37 79.18 Green
322 179.93 86.75 Green
323 169.18 77.69 Blue
324 176.70 79.95 Brown
325 169.29 90.91 Grey
326 158.88 78.08 Brown
327 174.12 58.14 Grey
328 168.45 80.70 Green
329 173.57 84.83 Grey
330 179.28 85.01 Brown
331 183.59 82.01 Green
332 165.62 83.87 Brown
333 162.69 56.72 Grey
334 173.66 92.71 Green
335 179.64 79.57 Blue
336 168.64 74.41 Green
337 174.43 88.69 Green
338 166.78 61.58 Grey
339 163.64 87.59 Green
340 186.84 81.87 Grey
341 165.24 75.10 Grey
342 167.14 66.14 Green
343 174.05 96.75 Green
344 163.51 98.50 Blue
345 175.79 72.45 Brown
346 171.01 71.69 Brown
347 164.62 58.90 Grey
348 175.68 68.05 Brown
349 176.77 96.92 Brown
350 162.32 83.99 Brown
351 173.70 56.81 Brown
352 172.93 80.28 Grey
353 168.61 94.19 Grey
354 176.91 80.36 Grey
355 160.70 83.36 Grey
356 167.98 97.77 Grey
357 162.77 67.26 Blue
358 158.12 86.77 Blue
359 171.87 94.69 Grey
360 170.10 80.47 Brown
361 167.20 79.90 Blue
362 183.70 82.62 Grey
363 168.27 81.53 Grey
364 170.03 78.79 Grey
365 174.71 61.01 Green
366 178.51 53.70 Green
367 172.89 80.60 Green
368 168.74 91.06 Brown
369 178.29 75.62 Brown
370 173.19 66.80 Blue
371 167.83 66.51 Grey
372 174.86 81.57 Brown
373 173.28 97.85 Blue
374 172.99 70.33 Grey
375 174.49 81.50 Brown
376 173.29 65.67 Green
377 169.51 84.37 Brown
378 165.80 75.83 Grey
379 167.26 83.97 Brown
380 170.53 78.82 Green
381 170.55 82.34 Green
382 162.10 79.49 Grey
383 172.49 91.61 Brown
384 162.38 75.50 Brown
385 164.96 78.21 Blue
386 163.44 79.93 Blue
387 178.79 80.70 Blue
388 164.14 76.53 Green
389 166.66 84.05 Blue
390 166.51 91.38 Grey
391 170.61 66.21 Green
392 169.89 67.70 Grey
393 170.66 71.10 Green
394 169.49 82.90 Brown
395 166.81 62.58 Grey
396 175.14 75.43 Brown
397 180.87 66.95 Grey
398 170.47 65.54 Brown
399 167.77 95.26 Blue
400 174.17 78.90 Grey
401 170.55 84.37 Blue
402 172.84 90.33 Green
403 169.35 74.83 Brown
404 164.23 90.20 Grey
405 172.67 65.62 Grey
406 170.82 69.08 Brown
407 165.18 83.55 Green
408 171.27 89.26 Green
409 163.58 74.67 Blue
410 164.84 96.49 Brown
411 178.38 72.75 Green
412 169.55 64.93 Green
413 167.92 83.20 Green
414 173.36 85.59 Brown
415 160.95 85.21 Blue
416 168.65 62.40 Green
417 168.75 73.15 Blue
418 179.55 82.68 Grey
419 161.89 57.96 Brown
420 175.65 80.65 Brown
421 165.47 96.19 Brown
422 164.18 96.14 Grey
423 171.62 92.12 Blue
424 174.20 49.91 Blue
425 169.95 102.97 Brown
426 178.14 79.73 Grey
427 169.11 80.43 Green
428 169.25 65.83 Green
429 172.88 74.83 Brown
430 169.71 70.31 Grey
431 175.56 102.08 Green
432 164.93 87.96 Brown
433 160.95 94.27 Green
434 181.23 86.62 Green
435 172.28 84.64 Brown
436 162.44 93.87 Brown
437 167.71 76.42 Brown
438 162.95 67.76 Green
439 165.13 90.21 Blue
440 170.60 76.06 Grey
441 174.42 94.34 Brown
442 171.65 77.83 Brown
443 159.08 93.10 Blue
444 175.59 77.52 Green
445 175.25 87.17 Brown
446 164.45 72.13 Grey
447 165.70 78.43 Green
448 177.44 73.05 Green
449 165.38 67.84 Green
450 176.99 70.46 Green
451 170.39 67.09 Brown
452 166.57 91.38 Grey
453 172.82 68.10 Blue
454 168.16 72.40 Brown
455 172.82 65.64 Green
456 169.64 82.83 Green
457 171.44 90.25 Green
458 174.57 74.25 Green
459 174.51 65.74 Blue
460 169.95 77.54 Grey
461 171.57 77.25 Blue
462 170.67 62.43 Grey
463 164.33 86.06 Green
464 172.30 69.03 Green
465 179.54 83.27 Grey
466 168.73 77.11 Blue
467 161.32 82.66 Brown
468 167.86 55.88 Blue
469 173.25 81.95 Green
470 173.71 73.84 Grey
471 165.57 87.48 Blue
472 173.05 97.93 Brown
473 160.42 77.11 Green
474 165.87 94.18 Green
475 170.39 82.31 Green
476 166.75 68.31 Brown
477 174.79 96.29 Grey
478 168.30 74.32 Grey
479 162.33 91.23 Green
480 171.90 98.54 Grey
481 174.32 87.41 Green
482 165.82 84.77 Brown
483 170.04 76.77 Brown
484 165.42 87.66 Brown
485 175.39 71.75 Grey
486 170.48 70.26 Blue
487 177.64 68.22 Blue
488 169.96 68.88 Grey
489 173.12 63.29 Green
490 167.70 84.97 Grey
491 171.16 70.59 Grey
492 172.62 78.78 Brown
493 170.93 82.57 Blue
494 175.16 72.37 Green
495 173.66 77.56 Blue
496 173.72 89.47 Blue
497 174.55 75.51 Brown
498 159.71 71.37 Green
499 172.64 66.25 Grey
500 176.96 92.89 Grey
501 171.88 71.22 Blue
502 168.80 84.55 Green
503 166.37 82.40 Green
504 175.14 81.53 Green
505 162.24 81.25 Grey
506 171.79 82.91 Blue
507 170.51 77.46 Blue
508 161.52 83.76 Green
509 169.70 92.53 Brown
510 167.78 110.07 Blue
511 169.99 88.48 Grey
512 175.55 78.99 Green
513 169.81 70.73 Brown
514 166.76 84.66 Brown
515 165.33 78.33 Green
516 166.39 80.08 Brown
517 171.64 71.24 Blue
518 163.61 67.36 Green
519 172.39 76.97 Brown
520 165.34 70.36 Grey
521 165.27 83.07 Green
522 174.67 84.47 Brown
523 170.31 82.48 Brown
524 178.55 76.20 Blue
525 171.06 68.43 Green
526 168.11 70.29 Brown
527 170.99 86.12 Blue
528 172.66 68.44 Green
529 166.39 74.34 Grey
530 174.46 87.28 Blue
531 163.64 77.11 Green
532 157.41 85.06 Green
533 154.61 97.13 Grey
534 167.06 72.14 Blue
535 180.28 89.22 Grey
536 175.20 78.90 Brown
537 174.87 88.93 Green
538 171.15 87.27 Green
539 166.00 94.82 Blue
540 172.67 84.30 Green
541 164.34 67.49 Blue
542 175.42 76.07 Grey
543 160.89 74.23 Blue
544 174.51 97.14 Blue
545 172.30 95.31 Green
546 166.54 72.34 Grey
547 169.85 89.49 Blue
548 161.94 63.30 Grey
549 158.34 91.87 Grey
550 158.43 80.51 Brown
551 170.77 91.87 Brown
552 164.59 84.75 Blue
553 176.54 92.77 Brown
554 174.73 67.75 Green
555 170.47 72.00 Blue
556 168.88 93.24 Blue
557 179.55 80.26 Grey
558 178.48 90.06 Grey
559 172.51 102.07 Green
560 164.28 83.49 Grey
561 167.50 74.58 Blue
562 168.58 83.41 Green
563 170.71 85.21 Brown
564 184.37 76.77 Grey
565 169.32 91.02 Grey
566 171.06 96.57 Brown
567 169.69 53.36 Blue
568 174.35 68.96 Brown
569 167.17 94.71 Green
570 170.46 86.31 Grey
571 169.01 71.64 Grey
572 167.93 64.08 Green
573 166.23 74.51 Green
574 174.65 88.89 Brown
575 174.16 83.45 Green
576 170.63 77.42 Blue
577 171.90 71.04 Brown
578 175.57 94.73 Green
579 169.01 86.16 Brown
580 173.70 82.59 Grey
581 172.21 68.85 Green
582 179.96 74.46 Green
583 175.74 77.95 Grey
584 170.30 81.68 Green
585 167.47 91.02 Grey
586 174.49 92.21 Green
587 162.05 89.92 Blue
588 162.73 85.66 Blue
589 176.50 81.81 Green
590 170.47 66.83 Brown
591 168.99 67.76 Blue
592 166.01 81.39 Grey
593 174.22 79.73 Green
594 169.73 96.10 Blue
595 171.66 73.21 Brown
596 173.38 68.85 Grey
597 188.25 84.44 Blue
598 175.77 94.70 Grey
599 160.35 73.66 Blue
600 168.66 81.08 Blue
601 181.00 84.14 Grey
602 174.66 72.85 Green
603 172.61 96.05 Brown
604 176.34 87.32 Blue
605 179.29 69.02 Green
606 166.75 72.30 Blue
607 165.82 93.53 Brown
608 159.99 76.05 Green
609 160.80 66.03 Brown
610 159.81 80.15 Brown
611 175.91 75.45 Brown
612 164.70 88.89 Brown
613 157.24 98.48 Grey
614 179.08 76.13 Brown
615 170.88 77.28 Grey
616 175.53 73.23 Brown
617 170.51 91.44 Brown
618 176.23 67.72 Grey
619 167.19 77.89 Green
620 163.81 81.98 Green
621 174.19 65.49 Brown
622 168.34 77.07 Grey
623 175.10 66.71 Brown
624 173.33 88.22 Brown
625 167.70 84.18 Brown
626 171.60 99.76 Green
627 169.61 66.49 Grey
628 175.48 94.89 Green
629 172.28 81.70 Brown
630 173.51 77.71 Brown
631 167.42 69.23 Grey
632 175.96 65.64 Brown
633 175.40 92.16 Blue
634 175.42 76.67 Grey
635 172.64 95.54 Green
636 170.12 62.73 Blue
637 169.54 86.98 Green
638 175.30 67.32 Blue
639 182.82 66.79 Blue
640 174.22 78.29 Grey
641 169.65 80.57 Grey
642 178.15 85.04 Blue
643 166.86 85.93 Blue
644 171.57 96.61 Green
645 171.22 72.66 Green
646 167.94 76.47 Blue
647 180.09 68.31 Blue
648 171.73 81.18 Blue
649 166.56 83.09 Grey
650 167.41 88.29 Grey
651 175.40 80.04 Brown
652 164.46 80.57 Green
653 178.23 106.17 Blue
654 172.17 91.50 Brown
655 176.62 93.05 Brown
656 159.36 94.47 Brown
657 172.81 86.80 Brown
658 167.11 82.85 Grey
659 157.93 86.43 Green
660 167.11 93.58 Blue
661 169.07 63.40 Grey
662 179.47 81.76 Grey
663 170.70 77.11 Blue
664 162.80 84.31 Grey
665 170.61 86.15 Brown
666 175.70 85.18 Brown
667 175.00 74.49 Green
668 163.85 98.05 Green
669 169.38 80.18 Grey
670 166.17 80.55 Brown
671 176.85 80.80 Grey
672 165.04 76.78 Blue
673 165.13 77.15 Green
674 165.01 79.78 Green
675 166.86 80.82 Brown
676 165.27 85.50 Blue
677 167.99 90.62 Grey
678 166.23 71.18 Brown
679 168.14 74.51 Brown
680 171.24 80.40 Blue
681 166.18 85.52 Grey
682 172.34 70.08 Blue
683 172.89 73.56 Green
684 159.22 82.88 Blue
685 167.03 82.11 Brown
686 172.58 82.97 Brown
687 171.93 57.87 Green
688 174.82 85.18 Blue
689 163.01 77.36 Brown
690 163.47 72.93 Blue
691 174.32 96.13 Brown
692 173.48 94.66 Green
693 177.04 77.41 Blue
694 168.45 87.81 Green
695 179.30 79.91 Brown
696 170.65 63.84 Blue
697 177.32 76.08 Green
698 163.49 73.98 Blue
699 162.56 88.89 Green
700 172.94 76.76 Green
701 167.98 71.36 Blue
702 163.52 69.37 Blue
703 161.15 79.52 Brown
704 174.18 79.44 Brown
705 172.09 83.08 Grey
706 180.52 107.99 Blue
707 168.35 83.53 Grey
708 177.52 91.81 Brown
709 159.07 70.68 Brown
710 177.89 81.75 Blue
711 176.04 75.52 Brown
712 166.40 77.72 Green
713 169.30 99.25 Grey
714 171.37 86.47 Grey
715 173.96 72.22 Green
716 165.10 83.57 Green
717 170.04 93.69 Blue
718 175.37 73.83 Green
719 162.70 77.07 Blue
720 169.03 83.85 Blue
721 176.12 79.88 Brown
722 175.02 95.07 Brown
723 175.40 58.96 Green
724 178.09 75.07 Green
725 167.57 89.64 Grey
726 168.44 86.23 Grey
727 173.93 80.99 Blue
728 174.89 77.70 Brown
729 156.53 88.39 Brown
730 158.14 70.11 Brown
731 164.13 74.18 Blue
732 162.48 71.05 Green
733 170.65 75.90 Blue
734 173.64 97.98 Blue
735 163.60 88.85 Grey
736 167.72 56.80 Brown
737 165.53 84.12 Blue
738 174.03 96.02 Brown
739 169.97 89.34 Brown
740 171.01 97.04 Green
741 165.78 85.96 Grey
742 161.30 77.03 Green
743 170.30 94.04 Green
744 174.06 84.49 Grey
745 164.71 73.76 Grey
746 183.16 82.72 Grey
747 160.47 69.88 Grey
748 169.30 80.16 Green
749 175.44 79.51 Brown
750 178.04 80.34 Blue
751 162.16 71.61 Blue
752 166.09 73.22 Brown
753 175.17 78.84 Green
754 166.52 80.02 Green
755 168.56 73.31 Grey
756 177.83 57.53 Blue
757 164.00 88.43 Blue
758 177.22 72.83 Brown
759 173.28 102.77 Grey
760 164.22 80.22 Blue
761 155.98 64.47 Brown
762 173.27 78.72 Blue
763 166.90 91.96 Brown
764 167.67 86.33 Grey
765 173.07 71.86 Blue
766 165.79 73.90 Blue
767 173.32 85.84 Grey
768 173.62 79.60 Blue
769 178.43 82.33 Brown
770 166.43 84.32 Green
771 176.24 73.80 Grey
772 173.88 89.46 Grey
773 185.86 82.84 Green
774 175.13 89.08 Brown
775 180.87 78.42 Grey
776 166.25 65.14 Brown
777 181.24 87.06 Grey
778 179.81 77.56 Grey
779 168.53 65.11 Green
780 170.02 71.52 Green
781 160.43 69.97 Green
782 177.64 106.19 Brown
783 158.91 79.72 Brown
784 162.28 77.82 Grey
785 165.65 79.35 Blue
786 168.54 62.54 Brown
787 163.52 85.95 Brown
788 165.35 78.17 Brown
789 160.80 67.44 Brown
790 164.82 77.67 Blue
791 169.76 75.66 Brown
792 167.74 91.58 Green
793 175.02 102.07 Brown
794 172.94 71.63 Green
795 176.46 83.53 Brown
796 163.61 90.45 Green
797 162.93 88.14 Blue
798 169.66 78.51 Blue
799 172.08 89.28 Brown
800 168.64 56.73 Green
801 171.05 78.97 Grey
802 173.00 84.20 Blue
803 176.34 98.64 Brown
804 174.56 69.69 Blue
805 165.06 89.35 Blue
806 175.35 80.05 Green
807 170.67 74.61 Blue
808 171.08 83.10 Brown
809 162.40 74.51 Brown
810 167.09 86.55 Grey
811 170.37 60.87 Blue
812 169.15 92.79 Green
813 169.29 93.92 Brown
814 172.95 91.14 Green
815 171.43 93.27 Blue
816 182.10 71.53 Brown
817 174.14 89.15 Green
818 165.37 81.29 Blue
819 169.59 82.43 Brown
820 156.46 83.50 Grey
821 167.61 86.78 Grey
822 167.12 54.32 Grey
823 171.57 87.24 Grey
824 166.16 64.82 Blue
825 180.57 73.19 Grey
826 164.96 75.41 Grey
827 160.27 90.35 Green
828 166.88 74.58 Brown
829 172.41 79.12 Blue
830 169.02 70.03 Green
831 177.10 84.62 Blue
832 171.60 76.20 Brown
833 183.32 78.71 Grey
834 167.46 68.50 Brown
835 175.21 89.14 Blue
836 170.57 70.63 Green
837 166.51 71.71 Green
838 168.63 83.09 Brown
839 172.41 81.08 Blue
840 170.24 80.34 Green
841 161.83 85.54 Blue
842 170.02 96.96 Blue
843 161.81 65.76 Grey
844 174.08 78.51 Brown
845 171.57 70.70 Brown
846 169.15 78.60 Blue
847 174.66 93.96 Brown
848 169.44 86.31 Blue
849 167.62 59.49 Brown
850 170.56 84.20 Blue
851 167.27 99.71 Blue
852 170.30 71.73 Green
853 159.72 93.13 Grey
854 170.94 80.08 Blue
855 177.91 73.99 Brown
856 183.17 89.15 Blue
857 169.58 60.65 Brown
858 169.02 74.60 Green
859 169.84 88.44 Blue
860 164.25 76.94 Green
861 175.09 70.02 Brown
862 169.72 99.71 Brown
863 164.65 78.53 Grey
864 163.73 101.92 Brown
865 172.30 88.28 Grey
866 172.80 94.03 Green
867 168.10 76.24 Grey
868 176.73 96.87 Grey
869 179.96 89.42 Green
870 162.36 88.32 Blue
871 166.92 87.07 Green
872 166.98 95.35 Blue
873 170.66 93.51 Green
874 173.54 83.70 Brown
875 173.32 112.62 Green
876 179.45 81.16 Grey
877 162.46 80.36 Green
878 174.87 65.26 Brown
879 167.64 78.52 Blue
880 169.90 52.80 Blue
881 173.65 76.87 Brown
882 163.42 99.51 Brown
883 174.19 85.48 Blue
884 175.28 76.68 Blue
885 171.18 74.76 Grey
886 178.80 75.56 Brown
887 166.25 59.10 Green
888 181.95 70.32 Green
889 180.73 78.12 Grey
890 170.92 86.30 Green
891 175.89 67.84 Blue
892 166.53 68.21 Green
893 178.40 89.83 Green
894 167.08 66.22 Brown
895 168.89 83.46 Grey
896 166.17 81.65 Blue
897 175.35 89.62 Green
898 177.78 73.63 Brown
899 176.52 74.42 Green
900 170.87 88.80 Blue
901 179.33 63.84 Green
902 161.61 95.79 Brown
903 171.28 93.33 Blue
904 165.34 83.55 Blue
905 180.37 91.29 Blue
906 153.28 71.01 Blue
907 166.04 82.74 Brown
908 172.06 104.51 Blue
909 164.02 79.75 Grey
910 162.03 100.43 Grey
911 162.00 80.25 Green
912 172.32 86.13 Brown
913 166.23 85.21 Brown
914 173.16 59.53 Blue
915 170.50 70.11 Green
916 173.85 93.26 Green
917 164.85 85.55 Green
918 173.25 63.75 Green
919 169.15 69.73 Brown
920 157.21 71.47 Brown
921 159.41 92.18 Brown
922 166.56 69.44 Blue
923 173.37 63.75 Blue
924 174.57 87.05 Blue
925 168.76 63.41 Brown
926 165.46 102.09 Green
927 167.50 92.33 Green
928 165.01 83.18 Brown
929 179.95 79.66 Green
930 161.27 76.53 Grey
931 173.19 77.02 Grey
932 181.25 84.35 Green
933 160.85 97.77 Grey
934 178.34 99.37 Blue
935 175.47 61.51 Green
936 166.91 75.59 Green
937 176.24 83.64 Blue
938 175.39 84.77 Grey
939 174.57 79.02 Blue
940 161.96 82.13 Green
941 176.83 92.57 Brown
942 176.98 80.37 Green
943 158.42 71.39 Brown
944 170.33 83.45 Blue
945 163.39 74.52 Blue
946 171.27 72.61 Green
947 171.78 96.39 Green
948 163.85 62.99 Green
949 168.51 84.79 Green
950 171.97 75.32 Brown
951 158.24 71.69 Brown
952 162.50 69.17 Blue
953 173.45 78.21 Green
954 173.29 81.38 Green
955 164.18 85.96 Grey
956 167.20 71.46 Green
957 166.23 80.14 Grey
958 175.09 84.00 Blue
959 168.60 89.17 Green
960 172.15 75.25 Grey
961 170.39 90.51 Brown
962 162.02 83.10 Green
963 172.22 80.60 Blue
964 170.00 75.17 Brown
965 172.25 67.77 Blue
966 169.11 90.02 Brown
967 175.82 81.91 Blue
968 176.32 64.98 Blue
969 158.69 63.33 Blue
970 175.24 87.27 Green
971 167.59 79.81 Green
972 173.04 74.40 Blue
973 156.81 67.87 Grey
974 172.93 48.17 Green
975 162.12 76.28 Grey
976 166.82 80.18 Blue
977 164.04 69.34 Grey
978 162.54 74.71 Blue
979 158.24 77.83 Green
980 181.20 83.56 Brown
981 165.45 64.38 Brown
982 166.78 86.86 Brown
983 170.50 80.14 Grey
984 182.66 71.01 Green
985 172.82 73.91 Green
986 165.98 92.00 Blue
987 164.48 84.56 Blue
988 172.20 83.71 Green
989 163.75 92.64 Blue
990 164.20 94.50 Grey
991 170.15 92.79 Blue
992 170.21 94.71 Brown
993 170.81 89.45 Green
994 163.78 74.79 Green
995 181.22 80.05 Brown
996 168.46 60.82 Grey
997 171.10 76.09 Brown
998 166.38 80.79 Blue
999 167.71 101.82 Green
1000 171.45 81.83 Grey

Random assignment

I’m now going to flip (an imaginary, computer-generated) coin for each of these 1,000 individuals to assigned them to group A or B:

ID Height Weight Eye colour Group
1 173.45 73.86 Brown A
2 171.20 82.76 Brown B
3 169.17 89.81 Blue A
4 160.84 84.11 Green B
5 168.63 61.80 Blue B
6 173.98 61.88 Grey A
7 175.75 84.49 Brown B
8 168.20 91.06 Green B
9 169.30 80.46 Grey A
10 170.34 76.69 Brown A
11 175.33 91.66 Brown A
12 167.36 72.74 Grey B
13 166.85 75.69 Blue B
14 174.38 81.74 Blue A
15 168.31 82.23 Green B
16 164.81 92.85 Blue B
17 171.25 60.05 Blue B
18 165.36 67.49 Brown A
19 160.41 88.42 Blue A
20 160.96 107.84 Brown A
21 167.34 89.94 Blue B
22 171.54 79.48 Grey B
23 173.57 89.41 Blue B
24 173.71 88.52 Brown B
25 172.66 79.96 Brown A
26 169.52 88.86 Brown A
27 163.50 68.28 Blue A
28 168.48 81.98 Blue A
29 164.35 87.85 Blue B
30 162.19 75.48 Blue B
31 178.65 109.53 Green A
32 189.11 78.97 Blue A
33 183.09 94.75 Brown B
34 167.40 69.23 Blue B
35 172.81 94.88 Grey B
36 166.64 85.56 Green A
37 162.36 93.31 Grey B
38 177.32 103.56 Green A
39 168.89 92.06 Brown A
40 167.62 91.22 Grey A
41 169.44 82.05 Brown A
42 174.97 68.02 Blue A
43 163.78 73.14 Brown B
44 171.69 85.26 Blue A
45 174.44 74.24 Brown B
46 170.05 83.29 Green B
47 174.65 95.44 Grey A
48 179.14 86.37 Green B
49 165.76 86.68 Brown B
50 182.30 87.00 Green A
51 162.06 67.21 Green B
52 178.82 77.39 Brown B
53 178.98 77.95 Grey B
54 179.42 70.76 Brown A
55 153.02 82.95 Grey B
56 170.71 82.41 Green B
57 162.25 101.52 Blue A
58 175.05 81.48 Grey A
59 171.09 99.20 Green A
60 175.87 71.32 Blue A
61 174.60 99.47 Blue A
62 164.20 95.72 Blue B
63 174.43 89.02 Blue B
64 174.93 94.43 Brown B
65 163.43 76.36 Grey B
66 173.69 82.44 Brown A
67 167.03 95.10 Brown B
68 180.92 65.69 Grey A
69 166.13 74.62 Grey B
70 170.61 79.36 Brown A
71 171.89 85.33 Grey B
72 174.60 75.08 Brown A
73 161.76 96.19 Blue A
74 166.41 79.60 Brown B
75 159.30 85.65 Grey B
76 170.68 68.50 Grey A
77 178.82 103.01 Brown A
78 171.23 72.80 Blue B
79 171.87 86.64 Brown A
80 167.73 86.78 Blue A
81 152.91 58.76 Grey A
82 165.75 80.79 Green A
83 180.13 78.20 Brown A
84 166.88 68.26 Green A
85 174.90 78.43 Brown B
86 160.65 92.92 Grey A
87 170.25 82.33 Grey B
88 169.09 84.70 Brown B
89 168.24 79.26 Grey B
90 154.54 79.51 Grey B
91 166.62 95.73 Blue B
92 166.42 80.47 Blue A
93 162.24 98.14 Brown A
94 170.64 66.14 Brown A
95 168.31 68.54 Grey B
96 174.19 89.41 Brown A
97 168.03 65.94 Green A
98 175.91 78.36 Grey A
99 165.17 78.72 Grey A
100 169.90 83.44 Blue A
101 161.45 55.73 Green A
102 167.96 65.53 Grey B
103 174.53 95.19 Green A
104 168.39 59.57 Brown A
105 168.84 86.82 Brown A
106 172.64 69.87 Grey A
107 161.84 94.73 Blue A
108 174.74 73.80 Green B
109 169.04 76.86 Green B
110 163.32 87.11 Green A
111 162.61 96.64 Brown A
112 158.09 81.20 Green B
113 162.54 76.78 Blue A
114 163.32 89.73 Blue A
115 182.62 80.61 Green A
116 167.86 71.94 Grey A
117 160.94 96.77 Brown B
118 160.88 88.32 Grey A
119 174.88 76.31 Grey A
120 174.63 77.30 Blue A
121 171.78 67.83 Brown B
122 162.31 104.22 Blue A
123 168.01 75.26 Brown A
124 173.51 90.91 Brown A
125 176.61 79.92 Green B
126 183.67 76.64 Blue A
127 172.52 60.35 Grey A
128 175.89 60.79 Blue A
129 179.04 92.83 Grey A
130 171.05 84.72 Blue B
131 175.13 90.78 Green A
132 170.60 66.63 Blue A
133 178.41 80.15 Green A
134 169.75 101.33 Green A
135 174.22 81.59 Blue A
136 163.76 88.59 Green A
137 163.97 74.97 Blue A
138 169.01 69.57 Grey A
139 163.66 66.33 Grey A
140 178.45 86.64 Green B
141 161.76 74.41 Grey A
142 165.75 89.09 Grey A
143 167.26 79.58 Green B
144 171.72 65.73 Green B
145 153.68 83.54 Green A
146 178.65 80.13 Blue B
147 170.01 74.77 Blue B
148 180.43 78.88 Blue A
149 172.31 90.28 Green A
150 172.52 69.81 Brown B
151 180.87 81.44 Grey B
152 171.10 82.99 Brown B
153 167.91 92.30 Grey A
154 180.24 88.78 Green A
155 163.82 92.91 Blue B
156 183.38 101.13 Brown B
157 166.42 66.69 Brown A
158 168.02 78.51 Grey B
159 167.82 72.85 Blue A
160 171.99 85.06 Blue B
161 174.39 84.77 Blue B
162 170.32 75.92 Brown A
163 164.61 71.85 Grey B
164 175.64 68.39 Green B
165 164.83 102.98 Green A
166 170.33 57.28 Blue B
167 161.23 77.74 Green B
168 173.52 73.38 Green A
169 176.69 63.00 Green B
170 164.07 98.37 Blue B
171 172.38 93.84 Blue A
172 166.35 72.34 Brown A
173 170.80 98.98 Blue A
174 168.92 58.21 Grey B
175 173.46 82.15 Green A
176 169.92 76.43 Blue A
177 166.77 87.38 Green A
178 170.77 85.85 Brown B
179 176.61 93.23 Grey B
180 174.08 61.97 Grey A
181 174.91 82.72 Brown B
182 172.56 77.29 Blue A
183 159.82 96.85 Brown A
184 162.81 70.48 Blue B
185 167.02 79.58 Brown A
186 174.08 63.44 Brown B
187 173.42 77.79 Green A
188 172.97 86.20 Green B
189 179.27 81.40 Blue A
190 174.08 76.52 Brown A
191 174.11 100.66 Grey B
192 154.08 88.66 Blue B
193 168.62 94.02 Brown A
194 178.32 77.77 Brown A
195 157.79 83.08 Blue B
196 167.62 86.16 Green A
197 164.88 86.24 Blue A
198 175.96 79.34 Blue B
199 167.30 100.40 Grey B
200 165.43 88.86 Green B
201 173.86 77.92 Brown B
202 172.50 90.38 Brown B
203 170.04 76.45 Grey B
204 167.18 97.95 Blue B
205 167.91 72.21 Grey B
206 178.22 76.72 Grey A
207 176.15 79.42 Grey A
208 172.54 94.96 Grey A
209 178.82 60.34 Brown A
210 166.46 66.00 Blue B
211 173.58 64.05 Grey B
212 159.74 68.48 Brown A
213 171.41 70.93 Grey A
214 171.62 84.84 Blue B
215 176.97 87.27 Brown A
216 175.78 79.58 Grey A
217 166.73 91.19 Green B
218 157.30 84.93 Brown A
219 171.34 75.14 Blue B
220 174.03 77.78 Blue B
221 165.89 79.50 Brown B
222 169.68 61.93 Grey B
223 167.15 91.26 Blue B
224 168.99 83.72 Green A
225 162.50 79.92 Green B
226 168.25 93.30 Grey B
227 158.27 76.53 Grey A
228 166.77 84.01 Grey A
229 168.67 77.13 Blue B
230 164.65 89.50 Grey A
231 177.11 86.97 Green B
232 164.51 88.50 Grey A
233 164.53 76.64 Grey A
234 170.51 64.43 Brown B
235 168.39 84.78 Green B
236 175.22 84.01 Green A
237 172.70 86.52 Grey A
238 174.97 88.79 Green A
239 164.25 88.15 Blue A
240 172.24 83.19 Grey A
241 170.10 83.14 Green B
242 174.25 67.54 Green A
243 167.71 77.09 Blue B
244 161.36 82.99 Brown A
245 168.73 67.83 Grey B
246 170.17 81.58 Grey A
247 163.32 60.32 Brown A
248 161.34 64.74 Blue B
249 171.71 65.06 Blue B
250 173.65 71.28 Grey B
251 175.38 77.53 Green A
252 171.41 93.20 Blue B
253 162.23 71.87 Green B
254 165.28 71.08 Green B
255 176.03 73.84 Blue B
256 166.92 90.06 Blue A
257 171.92 79.80 Brown A
258 179.09 69.54 Grey A
259 165.17 72.89 Grey A
260 176.35 72.22 Brown B
261 169.70 96.82 Blue B
262 180.08 80.36 Brown B
263 163.58 67.68 Blue A
264 160.75 75.41 Grey B
265 167.63 80.69 Brown B
266 165.63 76.11 Green B
267 163.03 66.29 Blue B
268 169.24 82.12 Green A
269 179.12 66.83 Grey A
270 166.23 69.41 Blue A
271 175.88 80.03 Grey A
272 163.63 89.07 Blue B
273 178.82 74.74 Brown A
274 162.15 80.24 Grey A
275 171.92 82.73 Brown B
276 169.85 68.37 Grey B
277 161.07 63.53 Blue A
278 176.34 60.49 Blue A
279 169.34 62.16 Brown A
280 169.73 62.84 Green A
281 178.60 68.12 Brown A
282 171.29 77.29 Brown A
283 163.97 84.08 Blue A
284 169.28 80.53 Blue A
285 184.22 85.39 Blue A
286 167.97 68.20 Brown B
287 173.72 87.45 Green B
288 181.11 71.78 Blue B
289 177.23 70.39 Brown A
290 180.28 79.57 Grey B
291 169.33 75.46 Green A
292 165.44 80.76 Brown A
293 172.72 82.62 Brown A
294 169.79 95.60 Blue B
295 179.75 94.71 Grey A
296 171.56 68.92 Brown A
297 167.61 84.67 Green B
298 167.04 80.70 Green A
299 174.10 70.29 Green A
300 158.37 63.09 Blue A
301 179.77 98.14 Brown A
302 175.21 82.67 Blue A
303 168.50 91.33 Brown A
304 168.49 100.35 Blue A
305 169.18 88.89 Brown A
306 165.83 84.71 Brown A
307 165.24 64.29 Green B
308 176.84 62.44 Grey B
309 166.06 86.83 Grey B
310 173.62 79.87 Grey A
311 168.91 109.09 Blue A
312 168.28 95.76 Blue B
313 163.57 87.42 Grey A
314 171.68 71.21 Green B
315 173.75 90.77 Blue B
316 158.63 82.57 Grey B
317 167.24 82.08 Green A
318 165.27 78.51 Blue A
319 184.60 54.18 Blue B
320 160.77 72.17 Grey B
321 183.37 79.18 Green A
322 179.93 86.75 Green A
323 169.18 77.69 Blue A
324 176.70 79.95 Brown B
325 169.29 90.91 Grey B
326 158.88 78.08 Brown B
327 174.12 58.14 Grey B
328 168.45 80.70 Green A
329 173.57 84.83 Grey B
330 179.28 85.01 Brown B
331 183.59 82.01 Green B
332 165.62 83.87 Brown B
333 162.69 56.72 Grey A
334 173.66 92.71 Green A
335 179.64 79.57 Blue B
336 168.64 74.41 Green B
337 174.43 88.69 Green B
338 166.78 61.58 Grey B
339 163.64 87.59 Green A
340 186.84 81.87 Grey A
341 165.24 75.10 Grey A
342 167.14 66.14 Green B
343 174.05 96.75 Green A
344 163.51 98.50 Blue A
345 175.79 72.45 Brown A
346 171.01 71.69 Brown B
347 164.62 58.90 Grey B
348 175.68 68.05 Brown B
349 176.77 96.92 Brown B
350 162.32 83.99 Brown B
351 173.70 56.81 Brown A
352 172.93 80.28 Grey B
353 168.61 94.19 Grey B
354 176.91 80.36 Grey A
355 160.70 83.36 Grey B
356 167.98 97.77 Grey A
357 162.77 67.26 Blue A
358 158.12 86.77 Blue A
359 171.87 94.69 Grey A
360 170.10 80.47 Brown B
361 167.20 79.90 Blue A
362 183.70 82.62 Grey B
363 168.27 81.53 Grey A
364 170.03 78.79 Grey B
365 174.71 61.01 Green B
366 178.51 53.70 Green A
367 172.89 80.60 Green B
368 168.74 91.06 Brown A
369 178.29 75.62 Brown B
370 173.19 66.80 Blue B
371 167.83 66.51 Grey B
372 174.86 81.57 Brown A
373 173.28 97.85 Blue B
374 172.99 70.33 Grey B
375 174.49 81.50 Brown A
376 173.29 65.67 Green A
377 169.51 84.37 Brown B
378 165.80 75.83 Grey B
379 167.26 83.97 Brown B
380 170.53 78.82 Green A
381 170.55 82.34 Green A
382 162.10 79.49 Grey A
383 172.49 91.61 Brown A
384 162.38 75.50 Brown A
385 164.96 78.21 Blue B
386 163.44 79.93 Blue A
387 178.79 80.70 Blue B
388 164.14 76.53 Green A
389 166.66 84.05 Blue B
390 166.51 91.38 Grey A
391 170.61 66.21 Green B
392 169.89 67.70 Grey B
393 170.66 71.10 Green A
394 169.49 82.90 Brown B
395 166.81 62.58 Grey B
396 175.14 75.43 Brown B
397 180.87 66.95 Grey B
398 170.47 65.54 Brown B
399 167.77 95.26 Blue A
400 174.17 78.90 Grey A
401 170.55 84.37 Blue A
402 172.84 90.33 Green B
403 169.35 74.83 Brown A
404 164.23 90.20 Grey A
405 172.67 65.62 Grey A
406 170.82 69.08 Brown B
407 165.18 83.55 Green A
408 171.27 89.26 Green B
409 163.58 74.67 Blue B
410 164.84 96.49 Brown B
411 178.38 72.75 Green B
412 169.55 64.93 Green A
413 167.92 83.20 Green A
414 173.36 85.59 Brown B
415 160.95 85.21 Blue A
416 168.65 62.40 Green A
417 168.75 73.15 Blue A
418 179.55 82.68 Grey B
419 161.89 57.96 Brown B
420 175.65 80.65 Brown B
421 165.47 96.19 Brown B
422 164.18 96.14 Grey B
423 171.62 92.12 Blue B
424 174.20 49.91 Blue A
425 169.95 102.97 Brown A
426 178.14 79.73 Grey B
427 169.11 80.43 Green A
428 169.25 65.83 Green B
429 172.88 74.83 Brown B
430 169.71 70.31 Grey A
431 175.56 102.08 Green A
432 164.93 87.96 Brown B
433 160.95 94.27 Green B
434 181.23 86.62 Green B
435 172.28 84.64 Brown B
436 162.44 93.87 Brown A
437 167.71 76.42 Brown A
438 162.95 67.76 Green A
439 165.13 90.21 Blue A
440 170.60 76.06 Grey B
441 174.42 94.34 Brown A
442 171.65 77.83 Brown B
443 159.08 93.10 Blue A
444 175.59 77.52 Green B
445 175.25 87.17 Brown A
446 164.45 72.13 Grey B
447 165.70 78.43 Green B
448 177.44 73.05 Green A
449 165.38 67.84 Green A
450 176.99 70.46 Green B
451 170.39 67.09 Brown A
452 166.57 91.38 Grey A
453 172.82 68.10 Blue B
454 168.16 72.40 Brown A
455 172.82 65.64 Green B
456 169.64 82.83 Green B
457 171.44 90.25 Green B
458 174.57 74.25 Green A
459 174.51 65.74 Blue B
460 169.95 77.54 Grey A
461 171.57 77.25 Blue A
462 170.67 62.43 Grey B
463 164.33 86.06 Green B
464 172.30 69.03 Green A
465 179.54 83.27 Grey A
466 168.73 77.11 Blue B
467 161.32 82.66 Brown A
468 167.86 55.88 Blue A
469 173.25 81.95 Green B
470 173.71 73.84 Grey B
471 165.57 87.48 Blue B
472 173.05 97.93 Brown A
473 160.42 77.11 Green A
474 165.87 94.18 Green B
475 170.39 82.31 Green A
476 166.75 68.31 Brown B
477 174.79 96.29 Grey A
478 168.30 74.32 Grey B
479 162.33 91.23 Green A
480 171.90 98.54 Grey A
481 174.32 87.41 Green A
482 165.82 84.77 Brown B
483 170.04 76.77 Brown A
484 165.42 87.66 Brown B
485 175.39 71.75 Grey A
486 170.48 70.26 Blue B
487 177.64 68.22 Blue A
488 169.96 68.88 Grey A
489 173.12 63.29 Green B
490 167.70 84.97 Grey A
491 171.16 70.59 Grey A
492 172.62 78.78 Brown B
493 170.93 82.57 Blue A
494 175.16 72.37 Green B
495 173.66 77.56 Blue A
496 173.72 89.47 Blue A
497 174.55 75.51 Brown B
498 159.71 71.37 Green B
499 172.64 66.25 Grey B
500 176.96 92.89 Grey A
501 171.88 71.22 Blue B
502 168.80 84.55 Green B
503 166.37 82.40 Green A
504 175.14 81.53 Green B
505 162.24 81.25 Grey B
506 171.79 82.91 Blue A
507 170.51 77.46 Blue B
508 161.52 83.76 Green B
509 169.70 92.53 Brown A
510 167.78 110.07 Blue B
511 169.99 88.48 Grey A
512 175.55 78.99 Green A
513 169.81 70.73 Brown B
514 166.76 84.66 Brown B
515 165.33 78.33 Green A
516 166.39 80.08 Brown B
517 171.64 71.24 Blue A
518 163.61 67.36 Green B
519 172.39 76.97 Brown A
520 165.34 70.36 Grey B
521 165.27 83.07 Green B
522 174.67 84.47 Brown B
523 170.31 82.48 Brown A
524 178.55 76.20 Blue A
525 171.06 68.43 Green B
526 168.11 70.29 Brown B
527 170.99 86.12 Blue A
528 172.66 68.44 Green B
529 166.39 74.34 Grey B
530 174.46 87.28 Blue B
531 163.64 77.11 Green A
532 157.41 85.06 Green B
533 154.61 97.13 Grey A
534 167.06 72.14 Blue B
535 180.28 89.22 Grey A
536 175.20 78.90 Brown A
537 174.87 88.93 Green A
538 171.15 87.27 Green B
539 166.00 94.82 Blue B
540 172.67 84.30 Green B
541 164.34 67.49 Blue A
542 175.42 76.07 Grey A
543 160.89 74.23 Blue A
544 174.51 97.14 Blue A
545 172.30 95.31 Green A
546 166.54 72.34 Grey B
547 169.85 89.49 Blue B
548 161.94 63.30 Grey A
549 158.34 91.87 Grey A
550 158.43 80.51 Brown A
551 170.77 91.87 Brown B
552 164.59 84.75 Blue B
553 176.54 92.77 Brown A
554 174.73 67.75 Green B
555 170.47 72.00 Blue A
556 168.88 93.24 Blue B
557 179.55 80.26 Grey B
558 178.48 90.06 Grey A
559 172.51 102.07 Green A
560 164.28 83.49 Grey B
561 167.50 74.58 Blue B
562 168.58 83.41 Green B
563 170.71 85.21 Brown A
564 184.37 76.77 Grey A
565 169.32 91.02 Grey B
566 171.06 96.57 Brown A
567 169.69 53.36 Blue B
568 174.35 68.96 Brown B
569 167.17 94.71 Green A
570 170.46 86.31 Grey A
571 169.01 71.64 Grey B
572 167.93 64.08 Green A
573 166.23 74.51 Green B
574 174.65 88.89 Brown A
575 174.16 83.45 Green B
576 170.63 77.42 Blue A
577 171.90 71.04 Brown A
578 175.57 94.73 Green A
579 169.01 86.16 Brown A
580 173.70 82.59 Grey A
581 172.21 68.85 Green B
582 179.96 74.46 Green B
583 175.74 77.95 Grey B
584 170.30 81.68 Green B
585 167.47 91.02 Grey B
586 174.49 92.21 Green A
587 162.05 89.92 Blue B
588 162.73 85.66 Blue A
589 176.50 81.81 Green A
590 170.47 66.83 Brown B
591 168.99 67.76 Blue A
592 166.01 81.39 Grey B
593 174.22 79.73 Green A
594 169.73 96.10 Blue A
595 171.66 73.21 Brown B
596 173.38 68.85 Grey A
597 188.25 84.44 Blue A
598 175.77 94.70 Grey A
599 160.35 73.66 Blue B
600 168.66 81.08 Blue A
601 181.00 84.14 Grey B
602 174.66 72.85 Green B
603 172.61 96.05 Brown A
604 176.34 87.32 Blue B
605 179.29 69.02 Green B
606 166.75 72.30 Blue A
607 165.82 93.53 Brown A
608 159.99 76.05 Green B
609 160.80 66.03 Brown A
610 159.81 80.15 Brown B
611 175.91 75.45 Brown A
612 164.70 88.89 Brown B
613 157.24 98.48 Grey A
614 179.08 76.13 Brown A
615 170.88 77.28 Grey A
616 175.53 73.23 Brown A
617 170.51 91.44 Brown A
618 176.23 67.72 Grey B
619 167.19 77.89 Green B
620 163.81 81.98 Green A
621 174.19 65.49 Brown B
622 168.34 77.07 Grey A
623 175.10 66.71 Brown B
624 173.33 88.22 Brown B
625 167.70 84.18 Brown B
626 171.60 99.76 Green A
627 169.61 66.49 Grey B
628 175.48 94.89 Green A
629 172.28 81.70 Brown B
630 173.51 77.71 Brown B
631 167.42 69.23 Grey A
632 175.96 65.64 Brown B
633 175.40 92.16 Blue B
634 175.42 76.67 Grey A
635 172.64 95.54 Green A
636 170.12 62.73 Blue B
637 169.54 86.98 Green B
638 175.30 67.32 Blue B
639 182.82 66.79 Blue B
640 174.22 78.29 Grey B
641 169.65 80.57 Grey B
642 178.15 85.04 Blue B
643 166.86 85.93 Blue A
644 171.57 96.61 Green A
645 171.22 72.66 Green A
646 167.94 76.47 Blue A
647 180.09 68.31 Blue B
648 171.73 81.18 Blue A
649 166.56 83.09 Grey B
650 167.41 88.29 Grey A
651 175.40 80.04 Brown A
652 164.46 80.57 Green A
653 178.23 106.17 Blue B
654 172.17 91.50 Brown B
655 176.62 93.05 Brown B
656 159.36 94.47 Brown A
657 172.81 86.80 Brown B
658 167.11 82.85 Grey A
659 157.93 86.43 Green B
660 167.11 93.58 Blue B
661 169.07 63.40 Grey A
662 179.47 81.76 Grey B
663 170.70 77.11 Blue B
664 162.80 84.31 Grey B
665 170.61 86.15 Brown A
666 175.70 85.18 Brown B
667 175.00 74.49 Green B
668 163.85 98.05 Green B
669 169.38 80.18 Grey B
670 166.17 80.55 Brown A
671 176.85 80.80 Grey B
672 165.04 76.78 Blue A
673 165.13 77.15 Green A
674 165.01 79.78 Green B
675 166.86 80.82 Brown B
676 165.27 85.50 Blue A
677 167.99 90.62 Grey A
678 166.23 71.18 Brown B
679 168.14 74.51 Brown A
680 171.24 80.40 Blue B
681 166.18 85.52 Grey A
682 172.34 70.08 Blue B
683 172.89 73.56 Green A
684 159.22 82.88 Blue B
685 167.03 82.11 Brown B
686 172.58 82.97 Brown A
687 171.93 57.87 Green B
688 174.82 85.18 Blue B
689 163.01 77.36 Brown B
690 163.47 72.93 Blue B
691 174.32 96.13 Brown B
692 173.48 94.66 Green A
693 177.04 77.41 Blue A
694 168.45 87.81 Green A
695 179.30 79.91 Brown A
696 170.65 63.84 Blue B
697 177.32 76.08 Green B
698 163.49 73.98 Blue B
699 162.56 88.89 Green A
700 172.94 76.76 Green B
701 167.98 71.36 Blue B
702 163.52 69.37 Blue B
703 161.15 79.52 Brown B
704 174.18 79.44 Brown A
705 172.09 83.08 Grey A
706 180.52 107.99 Blue B
707 168.35 83.53 Grey A
708 177.52 91.81 Brown A
709 159.07 70.68 Brown A
710 177.89 81.75 Blue B
711 176.04 75.52 Brown A
712 166.40 77.72 Green B
713 169.30 99.25 Grey A
714 171.37 86.47 Grey B
715 173.96 72.22 Green B
716 165.10 83.57 Green B
717 170.04 93.69 Blue B
718 175.37 73.83 Green B
719 162.70 77.07 Blue A
720 169.03 83.85 Blue A
721 176.12 79.88 Brown A
722 175.02 95.07 Brown B
723 175.40 58.96 Green A
724 178.09 75.07 Green B
725 167.57 89.64 Grey A
726 168.44 86.23 Grey B
727 173.93 80.99 Blue B
728 174.89 77.70 Brown B
729 156.53 88.39 Brown B
730 158.14 70.11 Brown B
731 164.13 74.18 Blue A
732 162.48 71.05 Green A
733 170.65 75.90 Blue B
734 173.64 97.98 Blue B
735 163.60 88.85 Grey A
736 167.72 56.80 Brown A
737 165.53 84.12 Blue B
738 174.03 96.02 Brown A
739 169.97 89.34 Brown A
740 171.01 97.04 Green A
741 165.78 85.96 Grey B
742 161.30 77.03 Green A
743 170.30 94.04 Green A
744 174.06 84.49 Grey A
745 164.71 73.76 Grey B
746 183.16 82.72 Grey A
747 160.47 69.88 Grey B
748 169.30 80.16 Green B
749 175.44 79.51 Brown B
750 178.04 80.34 Blue A
751 162.16 71.61 Blue A
752 166.09 73.22 Brown B
753 175.17 78.84 Green A
754 166.52 80.02 Green B
755 168.56 73.31 Grey A
756 177.83 57.53 Blue A
757 164.00 88.43 Blue A
758 177.22 72.83 Brown A
759 173.28 102.77 Grey B
760 164.22 80.22 Blue A
761 155.98 64.47 Brown A
762 173.27 78.72 Blue B
763 166.90 91.96 Brown B
764 167.67 86.33 Grey A
765 173.07 71.86 Blue A
766 165.79 73.90 Blue B
767 173.32 85.84 Grey A
768 173.62 79.60 Blue A
769 178.43 82.33 Brown B
770 166.43 84.32 Green B
771 176.24 73.80 Grey B
772 173.88 89.46 Grey A
773 185.86 82.84 Green A
774 175.13 89.08 Brown A
775 180.87 78.42 Grey A
776 166.25 65.14 Brown B
777 181.24 87.06 Grey B
778 179.81 77.56 Grey B
779 168.53 65.11 Green B
780 170.02 71.52 Green B
781 160.43 69.97 Green B
782 177.64 106.19 Brown A
783 158.91 79.72 Brown B
784 162.28 77.82 Grey B
785 165.65 79.35 Blue B
786 168.54 62.54 Brown B
787 163.52 85.95 Brown A
788 165.35 78.17 Brown B
789 160.80 67.44 Brown A
790 164.82 77.67 Blue A
791 169.76 75.66 Brown A
792 167.74 91.58 Green A
793 175.02 102.07 Brown B
794 172.94 71.63 Green A
795 176.46 83.53 Brown A
796 163.61 90.45 Green A
797 162.93 88.14 Blue B
798 169.66 78.51 Blue A
799 172.08 89.28 Brown A
800 168.64 56.73 Green A
801 171.05 78.97 Grey B
802 173.00 84.20 Blue B
803 176.34 98.64 Brown A
804 174.56 69.69 Blue B
805 165.06 89.35 Blue A
806 175.35 80.05 Green A
807 170.67 74.61 Blue B
808 171.08 83.10 Brown A
809 162.40 74.51 Brown B
810 167.09 86.55 Grey B
811 170.37 60.87 Blue A
812 169.15 92.79 Green B
813 169.29 93.92 Brown A
814 172.95 91.14 Green B
815 171.43 93.27 Blue B
816 182.10 71.53 Brown A
817 174.14 89.15 Green A
818 165.37 81.29 Blue B
819 169.59 82.43 Brown A
820 156.46 83.50 Grey A
821 167.61 86.78 Grey B
822 167.12 54.32 Grey B
823 171.57 87.24 Grey B
824 166.16 64.82 Blue B
825 180.57 73.19 Grey B
826 164.96 75.41 Grey B
827 160.27 90.35 Green B
828 166.88 74.58 Brown B
829 172.41 79.12 Blue B
830 169.02 70.03 Green A
831 177.10 84.62 Blue B
832 171.60 76.20 Brown A
833 183.32 78.71 Grey B
834 167.46 68.50 Brown A
835 175.21 89.14 Blue A
836 170.57 70.63 Green B
837 166.51 71.71 Green B
838 168.63 83.09 Brown B
839 172.41 81.08 Blue A
840 170.24 80.34 Green B
841 161.83 85.54 Blue A
842 170.02 96.96 Blue B
843 161.81 65.76 Grey B
844 174.08 78.51 Brown A
845 171.57 70.70 Brown B
846 169.15 78.60 Blue A
847 174.66 93.96 Brown B
848 169.44 86.31 Blue A
849 167.62 59.49 Brown A
850 170.56 84.20 Blue B
851 167.27 99.71 Blue B
852 170.30 71.73 Green A
853 159.72 93.13 Grey B
854 170.94 80.08 Blue B
855 177.91 73.99 Brown A
856 183.17 89.15 Blue A
857 169.58 60.65 Brown B
858 169.02 74.60 Green A
859 169.84 88.44 Blue A
860 164.25 76.94 Green A
861 175.09 70.02 Brown B
862 169.72 99.71 Brown A
863 164.65 78.53 Grey B
864 163.73 101.92 Brown A
865 172.30 88.28 Grey B
866 172.80 94.03 Green B
867 168.10 76.24 Grey B
868 176.73 96.87 Grey B
869 179.96 89.42 Green B
870 162.36 88.32 Blue A
871 166.92 87.07 Green B
872 166.98 95.35 Blue B
873 170.66 93.51 Green B
874 173.54 83.70 Brown B
875 173.32 112.62 Green A
876 179.45 81.16 Grey A
877 162.46 80.36 Green A
878 174.87 65.26 Brown A
879 167.64 78.52 Blue A
880 169.90 52.80 Blue B
881 173.65 76.87 Brown A
882 163.42 99.51 Brown B
883 174.19 85.48 Blue B
884 175.28 76.68 Blue B
885 171.18 74.76 Grey A
886 178.80 75.56 Brown B
887 166.25 59.10 Green B
888 181.95 70.32 Green A
889 180.73 78.12 Grey A
890 170.92 86.30 Green B
891 175.89 67.84 Blue B
892 166.53 68.21 Green B
893 178.40 89.83 Green A
894 167.08 66.22 Brown A
895 168.89 83.46 Grey A
896 166.17 81.65 Blue A
897 175.35 89.62 Green A
898 177.78 73.63 Brown A
899 176.52 74.42 Green B
900 170.87 88.80 Blue B
901 179.33 63.84 Green B
902 161.61 95.79 Brown B
903 171.28 93.33 Blue A
904 165.34 83.55 Blue A
905 180.37 91.29 Blue B
906 153.28 71.01 Blue A
907 166.04 82.74 Brown A
908 172.06 104.51 Blue A
909 164.02 79.75 Grey B
910 162.03 100.43 Grey B
911 162.00 80.25 Green B
912 172.32 86.13 Brown A
913 166.23 85.21 Brown A
914 173.16 59.53 Blue B
915 170.50 70.11 Green B
916 173.85 93.26 Green B
917 164.85 85.55 Green B
918 173.25 63.75 Green B
919 169.15 69.73 Brown B
920 157.21 71.47 Brown B
921 159.41 92.18 Brown B
922 166.56 69.44 Blue B
923 173.37 63.75 Blue A
924 174.57 87.05 Blue B
925 168.76 63.41 Brown A
926 165.46 102.09 Green B
927 167.50 92.33 Green B
928 165.01 83.18 Brown A
929 179.95 79.66 Green B
930 161.27 76.53 Grey A
931 173.19 77.02 Grey A
932 181.25 84.35 Green A
933 160.85 97.77 Grey A
934 178.34 99.37 Blue B
935 175.47 61.51 Green A
936 166.91 75.59 Green A
937 176.24 83.64 Blue A
938 175.39 84.77 Grey A
939 174.57 79.02 Blue A
940 161.96 82.13 Green B
941 176.83 92.57 Brown B
942 176.98 80.37 Green A
943 158.42 71.39 Brown A
944 170.33 83.45 Blue B
945 163.39 74.52 Blue A
946 171.27 72.61 Green B
947 171.78 96.39 Green A
948 163.85 62.99 Green B
949 168.51 84.79 Green B
950 171.97 75.32 Brown B
951 158.24 71.69 Brown B
952 162.50 69.17 Blue B
953 173.45 78.21 Green B
954 173.29 81.38 Green A
955 164.18 85.96 Grey A
956 167.20 71.46 Green B
957 166.23 80.14 Grey A
958 175.09 84.00 Blue A
959 168.60 89.17 Green A
960 172.15 75.25 Grey B
961 170.39 90.51 Brown B
962 162.02 83.10 Green A
963 172.22 80.60 Blue B
964 170.00 75.17 Brown A
965 172.25 67.77 Blue A
966 169.11 90.02 Brown A
967 175.82 81.91 Blue B
968 176.32 64.98 Blue A
969 158.69 63.33 Blue B
970 175.24 87.27 Green A
971 167.59 79.81 Green A
972 173.04 74.40 Blue B
973 156.81 67.87 Grey B
974 172.93 48.17 Green B
975 162.12 76.28 Grey A
976 166.82 80.18 Blue A
977 164.04 69.34 Grey A
978 162.54 74.71 Blue B
979 158.24 77.83 Green B
980 181.20 83.56 Brown A
981 165.45 64.38 Brown B
982 166.78 86.86 Brown B
983 170.50 80.14 Grey B
984 182.66 71.01 Green B
985 172.82 73.91 Green A
986 165.98 92.00 Blue A
987 164.48 84.56 Blue A
988 172.20 83.71 Green B
989 163.75 92.64 Blue A
990 164.20 94.50 Grey A
991 170.15 92.79 Blue B
992 170.21 94.71 Brown A
993 170.81 89.45 Green A
994 163.78 74.79 Green A
995 181.22 80.05 Brown A
996 168.46 60.82 Grey A
997 171.10 76.09 Brown B
998 166.38 80.79 Blue A
999 167.71 101.82 Green A
1000 171.45 81.83 Grey B

How similar are these groups?

Let’s first check their heights:

How similar are these groups?

And their weights:

How similar are these groups?

And their eye colors:

Making sure this wasn’t a fluke

Let’s re-run this:

ID Height Weight Eye colour Group
1 173.45 73.86 Brown B
2 171.20 82.76 Brown B
3 169.17 89.81 Blue A
4 160.84 84.11 Green A
5 168.63 61.80 Blue A
6 173.98 61.88 Grey A
7 175.75 84.49 Brown A
8 168.20 91.06 Green A
9 169.30 80.46 Grey B
10 170.34 76.69 Brown B
11 175.33 91.66 Brown B
12 167.36 72.74 Grey B
13 166.85 75.69 Blue A
14 174.38 81.74 Blue A
15 168.31 82.23 Green A
16 164.81 92.85 Blue B
17 171.25 60.05 Blue B
18 165.36 67.49 Brown B
19 160.41 88.42 Blue A
20 160.96 107.84 Brown A
21 167.34 89.94 Blue B
22 171.54 79.48 Grey A
23 173.57 89.41 Blue A
24 173.71 88.52 Brown B
25 172.66 79.96 Brown B
26 169.52 88.86 Brown B
27 163.50 68.28 Blue B
28 168.48 81.98 Blue A
29 164.35 87.85 Blue A
30 162.19 75.48 Blue A
31 178.65 109.53 Green A
32 189.11 78.97 Blue A
33 183.09 94.75 Brown B
34 167.40 69.23 Blue B
35 172.81 94.88 Grey B
36 166.64 85.56 Green A
37 162.36 93.31 Grey A
38 177.32 103.56 Green A
39 168.89 92.06 Brown A
40 167.62 91.22 Grey A
41 169.44 82.05 Brown A
42 174.97 68.02 Blue B
43 163.78 73.14 Brown A
44 171.69 85.26 Blue A
45 174.44 74.24 Brown A
46 170.05 83.29 Green A
47 174.65 95.44 Grey B
48 179.14 86.37 Green B
49 165.76 86.68 Brown B
50 182.30 87.00 Green B
51 162.06 67.21 Green A
52 178.82 77.39 Brown B
53 178.98 77.95 Grey A
54 179.42 70.76 Brown A
55 153.02 82.95 Grey B
56 170.71 82.41 Green B
57 162.25 101.52 Blue B
58 175.05 81.48 Grey A
59 171.09 99.20 Green B
60 175.87 71.32 Blue B
61 174.60 99.47 Blue B
62 164.20 95.72 Blue B
63 174.43 89.02 Blue A
64 174.93 94.43 Brown B
65 163.43 76.36 Grey B
66 173.69 82.44 Brown B
67 167.03 95.10 Brown A
68 180.92 65.69 Grey B
69 166.13 74.62 Grey B
70 170.61 79.36 Brown A
71 171.89 85.33 Grey B
72 174.60 75.08 Brown B
73 161.76 96.19 Blue B
74 166.41 79.60 Brown B
75 159.30 85.65 Grey A
76 170.68 68.50 Grey A
77 178.82 103.01 Brown B
78 171.23 72.80 Blue A
79 171.87 86.64 Brown B
80 167.73 86.78 Blue A
81 152.91 58.76 Grey A
82 165.75 80.79 Green A
83 180.13 78.20 Brown A
84 166.88 68.26 Green A
85 174.90 78.43 Brown A
86 160.65 92.92 Grey A
87 170.25 82.33 Grey A
88 169.09 84.70 Brown A
89 168.24 79.26 Grey A
90 154.54 79.51 Grey B
91 166.62 95.73 Blue B
92 166.42 80.47 Blue B
93 162.24 98.14 Brown A
94 170.64 66.14 Brown A
95 168.31 68.54 Grey B
96 174.19 89.41 Brown B
97 168.03 65.94 Green B
98 175.91 78.36 Grey A
99 165.17 78.72 Grey A
100 169.90 83.44 Blue B
101 161.45 55.73 Green A
102 167.96 65.53 Grey B
103 174.53 95.19 Green A
104 168.39 59.57 Brown B
105 168.84 86.82 Brown A
106 172.64 69.87 Grey A
107 161.84 94.73 Blue A
108 174.74 73.80 Green A
109 169.04 76.86 Green B
110 163.32 87.11 Green B
111 162.61 96.64 Brown B
112 158.09 81.20 Green A
113 162.54 76.78 Blue B
114 163.32 89.73 Blue A
115 182.62 80.61 Green B
116 167.86 71.94 Grey A
117 160.94 96.77 Brown A
118 160.88 88.32 Grey B
119 174.88 76.31 Grey A
120 174.63 77.30 Blue B
121 171.78 67.83 Brown A
122 162.31 104.22 Blue A
123 168.01 75.26 Brown B
124 173.51 90.91 Brown B
125 176.61 79.92 Green B
126 183.67 76.64 Blue B
127 172.52 60.35 Grey A
128 175.89 60.79 Blue B
129 179.04 92.83 Grey B
130 171.05 84.72 Blue B
131 175.13 90.78 Green B
132 170.60 66.63 Blue A
133 178.41 80.15 Green B
134 169.75 101.33 Green A
135 174.22 81.59 Blue A
136 163.76 88.59 Green B
137 163.97 74.97 Blue B
138 169.01 69.57 Grey B
139 163.66 66.33 Grey B
140 178.45 86.64 Green A
141 161.76 74.41 Grey B
142 165.75 89.09 Grey A
143 167.26 79.58 Green B
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824 166.16 64.82 Blue B
825 180.57 73.19 Grey B
826 164.96 75.41 Grey A
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851 167.27 99.71 Blue A
852 170.30 71.73 Green A
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855 177.91 73.99 Brown A
856 183.17 89.15 Blue B
857 169.58 60.65 Brown A
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863 164.65 78.53 Grey B
864 163.73 101.92 Brown A
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866 172.80 94.03 Green A
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868 176.73 96.87 Grey B
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870 162.36 88.32 Blue B
871 166.92 87.07 Green A
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874 173.54 83.70 Brown B
875 173.32 112.62 Green B
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877 162.46 80.36 Green B
878 174.87 65.26 Brown A
879 167.64 78.52 Blue B
880 169.90 52.80 Blue B
881 173.65 76.87 Brown B
882 163.42 99.51 Brown A
883 174.19 85.48 Blue B
884 175.28 76.68 Blue A
885 171.18 74.76 Grey B
886 178.80 75.56 Brown B
887 166.25 59.10 Green B
888 181.95 70.32 Green A
889 180.73 78.12 Grey B
890 170.92 86.30 Green A
891 175.89 67.84 Blue A
892 166.53 68.21 Green A
893 178.40 89.83 Green B
894 167.08 66.22 Brown A
895 168.89 83.46 Grey B
896 166.17 81.65 Blue A
897 175.35 89.62 Green B
898 177.78 73.63 Brown B
899 176.52 74.42 Green B
900 170.87 88.80 Blue B
901 179.33 63.84 Green B
902 161.61 95.79 Brown B
903 171.28 93.33 Blue A
904 165.34 83.55 Blue A
905 180.37 91.29 Blue A
906 153.28 71.01 Blue A
907 166.04 82.74 Brown B
908 172.06 104.51 Blue B
909 164.02 79.75 Grey A
910 162.03 100.43 Grey B
911 162.00 80.25 Green B
912 172.32 86.13 Brown B
913 166.23 85.21 Brown A
914 173.16 59.53 Blue B
915 170.50 70.11 Green B
916 173.85 93.26 Green B
917 164.85 85.55 Green B
918 173.25 63.75 Green A
919 169.15 69.73 Brown A
920 157.21 71.47 Brown B
921 159.41 92.18 Brown A
922 166.56 69.44 Blue A
923 173.37 63.75 Blue B
924 174.57 87.05 Blue A
925 168.76 63.41 Brown B
926 165.46 102.09 Green B
927 167.50 92.33 Green B
928 165.01 83.18 Brown A
929 179.95 79.66 Green A
930 161.27 76.53 Grey A
931 173.19 77.02 Grey B
932 181.25 84.35 Green B
933 160.85 97.77 Grey A
934 178.34 99.37 Blue A
935 175.47 61.51 Green A
936 166.91 75.59 Green B
937 176.24 83.64 Blue B
938 175.39 84.77 Grey A
939 174.57 79.02 Blue A
940 161.96 82.13 Green B
941 176.83 92.57 Brown B
942 176.98 80.37 Green B
943 158.42 71.39 Brown B
944 170.33 83.45 Blue A
945 163.39 74.52 Blue B
946 171.27 72.61 Green A
947 171.78 96.39 Green A
948 163.85 62.99 Green B
949 168.51 84.79 Green B
950 171.97 75.32 Brown B
951 158.24 71.69 Brown A
952 162.50 69.17 Blue A
953 173.45 78.21 Green B
954 173.29 81.38 Green A
955 164.18 85.96 Grey B
956 167.20 71.46 Green A
957 166.23 80.14 Grey A
958 175.09 84.00 Blue A
959 168.60 89.17 Green A
960 172.15 75.25 Grey A
961 170.39 90.51 Brown B
962 162.02 83.10 Green B
963 172.22 80.60 Blue B
964 170.00 75.17 Brown A
965 172.25 67.77 Blue B
966 169.11 90.02 Brown A
967 175.82 81.91 Blue B
968 176.32 64.98 Blue B
969 158.69 63.33 Blue B
970 175.24 87.27 Green B
971 167.59 79.81 Green B
972 173.04 74.40 Blue B
973 156.81 67.87 Grey B
974 172.93 48.17 Green A
975 162.12 76.28 Grey B
976 166.82 80.18 Blue A
977 164.04 69.34 Grey B
978 162.54 74.71 Blue B
979 158.24 77.83 Green B
980 181.20 83.56 Brown B
981 165.45 64.38 Brown A
982 166.78 86.86 Brown A
983 170.50 80.14 Grey A
984 182.66 71.01 Green A
985 172.82 73.91 Green B
986 165.98 92.00 Blue B
987 164.48 84.56 Blue A
988 172.20 83.71 Green A
989 163.75 92.64 Blue B
990 164.20 94.50 Grey B
991 170.15 92.79 Blue B
992 170.21 94.71 Brown A
993 170.81 89.45 Green B
994 163.78 74.79 Green A
995 181.22 80.05 Brown B
996 168.46 60.82 Grey B
997 171.10 76.09 Brown A
998 166.38 80.79 Blue A
999 167.71 101.82 Green B
1000 171.45 81.83 Grey A

Check how similar they are

Increasingly similar

In fact, if we did this many, many, many times, these groups would be, on average, increasingly identical!

Why?

  • Central limit theorem

  • Law of large numbers

Do international monitors deter election-day fraud?

Yes!

  • The international community monitored the 2003 Armenian Presidential elections
  • Monitors were assigned randomly to the polling stations
  • Hyde found a big average difference between the vote share received by the cheating party at monitored stations compared to non-monitored stations.